Main Effects and Interactions in Mixed and Incomplete Data Frames

• 成果类型: Article
• 署名作者: Robin, Genevieve; Klopp, Olga; Josse, Julie; Moulines, Eric; Tibshirani, Robert
• 署名单位: Institut Polytechnique de Paris; Ecole Polytechnique; Inria; ESSEC Business School; Institut Polytechnique de Paris; ENSAE Paris; HSE University (National Research University Higher School of Economics); Stanford University; Stanford University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2019.1623041
• 发表日期: 2020
• 页码: 1292-1303

摘要

A mixed data frame (MDF) is a table collecting categorical, numerical, and count observations. The use of MDF is widespread in statistics and the applications are numerous from abundance data in ecology to recommender systems. In many cases, an MDF exhibits simultaneously main effects, such as row, column, or group effects and interactions, for which a low-rank model has often been suggested. Although the literature on low-rank approximations is very substantial, with few exceptions, existing methods do not allow to incorporate main effects and interactions while providing statistical guarantees. The present work fills this gap. We propose an estimation method which allows to recover simultaneously the main effects and the interactions. We show that our method is near optimal under conditions which are met in our targeted applications. We also propose an optimization algorithm which provably converges to an optimal solution. Numerical experiments reveal that our method, mimi, performs well when the main effects are sparse and the interaction matrix has low-rank. We also show that mimi compares favorably to existing methods, in particular when the main effects are significantly large compared to the interactions, and when the proportion of missing entries is large. The method is available as an R package on the Comprehensive R Archive Network. for this article are available online.